# Discount rate & NPV formulas

BearingPoint Case: Digital Business Model of a Parking App
New answer on Oct 16, 2020
1.5 k Views

Hey,

1) I am a little confused about the discount rate. Could anyone help me to understand the formula to calculate this discount rate
2) Which formula do you use after to calculate the NPV? (NPV = (Cash flows)/( 1+r)^t)?

Thanks!

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In nutshell:

Would you prefer to receive 1000 USD now or in one year? I guess now. So basically the 1000 USD in one year have a "smaller" value than 1000 USD now.

Let's build on that.

If I give you 1000 USD now, you could invest them, say at 5%.

So in one year you would have 1050 USD. This means that having 1000 USD now is the same as having 1050 USD in one year.

In formulas: 1050 USD in one year are equal to

1050 USD/(1+5%)^1 year

or

1050/(1+0,05), which gives 1000 USD as a result. The NPV of 1050 USD in one year is equal to 1000 USD now.

But what happens in two years?

If I give you 1000 USD now, then you could invest them at 5% rate per year. At the end of the first year you would have 1050 USD (see above), and at the end of the second year 1050*(1+0,05), or 1102,05 USD.

This means that 1000 USD now are like 1102,5 in two years. The discount rate of 5% must be applied for two periods, so 1102,5 USD/(1+5%)^2, or 1102,50/(1,05)^2, or 1102,50/1,1025 - equal to 1000 USD.

I hope this helps!

(edited)

I still dont understand why the discount rate decreases over the years? Can someone please clarify it with the example of the case? Would be very grateful for that.s?

Same question here! Considering the formula of NPV the reduction of the discount rate doesn't make any sense

@Evandro and @Nina - You need to be careful in defining the discount rate: The discount rate is the "divisor" of the PV-formula, hence the discount rate's formula is 1/(1+r)^t. Alternatively, you can define the discount rate by taking (1+r)^(-t), which leads to the same result. Applying this to the case, where r = WACC = 0.1, the discount rate formula is 1/(1+0.1)^t. Now, checking for different years (t), you will end up at the discount rates shown in table 8. Let's do the example of year 2020 (t=1): 1/(1.1)^1 = 0.9091 Hope this helps :)

(edited)

Nothing much to add to the other posts, just one thing:

Very few cases actually ask you to use this formula to calculate NPVs. And even if they do, there is sometimes a catch in the question that allows you to not actually calculat it.

To give an example: if you're comparing two projects. Project A has a lower nominal payment at a later stage than Project B, there might be the question regarding the NPV, but for the financial decision making it doesn't matter, because Project B will always be profitbale. You can state that and then discuss other, more qualitative considerations.